Over the past several years, astrophysical observations of neutron stars using X-rays and radio wavelengths have made significant progress towards determining the Equation of State of neutron star matter. The discovery of several interesting new pulsars as well as improved instrumentation has finally allowed us to start measuring the masses of millisecond pulsars. These systems have had potentially substantial amounts of mass accreted onto them during the "recycling" process and are likely more massive, on average, than the "canonical" 1.4 M_sun neutron stars found in Hulse-Taylor-like double neutron star binaries. The so-called Shapiro Delay has been used to make very precise measurements of 1.67 and 1.97 M_sun neutron stars in the past two years. These systems strongly constrain the equation of state of nuclear matter and a variety of other topics in physics/astrophysics. Finally, I'll show that there is good potential for more measurements in the near future.